Maths Problems with Solutions and Explanations for Grade 5

A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
SolutionThe number of chocolate bars is equal to
18 × 25 = 450

It takes John 25 minutes to walk to the car park and 45 to drive to work. At what time should he get out of the house in order to get to work at 9:00 a.m.?
SolutionThe time it takes John to get to work: time to walk to car park + time to drive
25 + 45 = 70 minutes = 1 hour and 10 minutes
John needs to get out of the house 1 hour and 10 minutes before 9:00 am at
9:00 - 1:10 = 7:50 a.m.

Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers?
SolutionThe time it takes Kim to walk 18 kilometers is equal to
18 / 4 = 4.5 hours = 4 hours + 0.5 × 60 minutes
= 4 hours and 30 minutes.

A factory produced 2300 TV sets in its first year of production. 4500 sets were produced in its second year and 500 more sets were produced in its third year than in its second year. How many TV sets were produced in three years?
Solution500 TV sets were produced in the third year than in the second year. The number of sets produced in the third year is equal to
4,500 + 500 = 5,000
The number of TV sets produced in three years is equal to
sum of the number of TV sets produced in each year
2,300 + 4,500 + 5,000 = 11,800

Linda bought 3 notebooks at $1.20 each; a box of pencils at $1.50 and a box of pens at $1.70. How much did Linda spend?
SolutionLinda spent
1.20 × 3 = $3.60 on notebooks
The total amount of money that Linda spent is equal to
3.60 + 1.50 + 1.70 = $6.80

Tom and Bob have a total of 49 toys. If Bob has 5 more toys than Tom, how many toys does each one have?
SolutionIf 5 toys are taken out of 49 toys and the remaining ones distributed to Tom and Bob, they will both have equal numbers of toys
49 - 5 = 44 for Tom and Bob
If distributed equally, each one will have
44 ÷ 2 = 22 toys
Bob has 5 more toys than Tom, so Bob has
22 + 5 = 27 toys
Bob has 27 and Tom has 22 toys and it is easy to check that between them they have 49 and the difference is 5.

John can eat a quarter of a pizza in one minute. How long does it take John to eat one pizza and a half?
Solution
2 possible solutions:
1) There are 4 quarters of a pizza in one pizza and there 2 quarters of a pizza in a half a pizza. So there is a total of 6 quarters in one pizza and a half. If John eats a quarter in one minutes, he needs 6 minutes to eat all 6 quarters.2) The above problem could also be solved by dividing the mixed number 1 and 1/2 by 1/4
1 (1/2) ÷ 1 / 4 = 3 / 2 × 4 / 1 = 6 minutes.

John can eat a sixth of a pizza in two minutes. It takes 3 minutes for Billy to eat one quarter of the same pizza. If John and Billy start eating one pizza each, who will finish first?
SolutionIn one pizza, there are 6 sixths and John will take .
2 × 6 = 12 minutes to finish one pizza
In one pizza, there are 4 quarters and Billy will take .
3 × 4 = 12 minutes to finish one pizza.
It takes each one of them 12 minutes and they will finish at the same time.

John read the quarter of the time that Tom read. Tom read only two-fifth of the time that Sasha read. Sasha read twice as long as Mike. If Mike read 5 hours, how long did John read?
SolutionMike read 5 hours. Sasha read twice as long as Mike. Hence Sasha read:
2 × 5 = 10 hours
Tom read two-fifths of the time that Sasha read. Hence Tom read:
(2 / 5) × 10 = 4 hours
John read the quarter of the time that Tom read. Hence John read:
(1 / 4) × 4 = 1 hour

Jim, Carla and Tomy are members of the same family. Carla is 5 years older than Jim. Tomy is 6 years older than Carla. The sum of their three ages is 31 years. How old is each one them?
SolutionThis problem can be solved using a table as shown below where Jim's age is guessed then Carla's and Tomy's ages are calculated. The calculations are stopped when the condition in the problem which is "the sum of their three ages is 31 years" is reached.

Jim's age

Carla's age

Tomy's age

The sum of all ages

1

1 + 5 = 6

6 + 6 = 12

1 + 6 + 12 = 19

2

2 + 5 =7

7 + 6 = 13

2+ 7 + 13 = 22

3

3 + 5 = 8

8 + 6 = 14

3 + 8 + 14 = 25

4

4 + 5 = 9

9 + 6 = 15

4 + 9 + 15 = 28

5

5 + 5 = 10

10 + 6 = 16

5 + 10 + 16 = 31

The column on the right, where all ages are added, shows whether the main condition ("The sum of their three ages is 31 years") is satisfied or not: last row of the table shows: Jim 5 , Carla 10 and Tomy 16 satisfy the condition in the problem.

Mel had $35 and withdraw some more money from his bank account. He bought a pair of trousers at $34.00, two shirts at $16.00 each and 2 pairs of shoes at $24.00 each. After the shopping, he had $32.00 left. How much money did Mel withdraw from the bank?

How many minutes are in one week?

In Tim's house, a rectangular swimming pool (blue) whose length 30 meters and width 10 meters is surrounded by grass (green). The pool with the grassy area make a large rectangle whose length is 50 meters and width 20 meters. What area is occupied by the grass?

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Mary wants to make a box. She starts with a piece of cardboard whose length is 15 centimeters and with is 10 centimeters. Then she cuts congruent squares with side of 3 centimeters at the four corners. What is the area of the cardboard after she cuts the 4 corners?

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A painter charges $ 225 for materials and $ 35 per hour for labour. The total cost of painting an office is $ 330. How many hours did it take the painter to paint the office?

Three toy cars and 4 toy trains cost $18. Two toy cars and 3 toy trains cost $13. What is the price of one toy car and the price of one toy train if both prices are whole numbers of Dollars? (Hint: Use a table)